Reduce to lowest terms: $ \dfrac{2}{7} \div \dfrac{8}{5} = {?}$
Explanation: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{8}{5}$ is $ \dfrac{5}{8}$ Therefore: $ \dfrac{2}{7} \div \dfrac{8}{5} = \dfrac{2}{7} \times \dfrac{5}{8} $ $ \phantom{ \dfrac{2}{7} \times \dfrac{5}{8}} = \dfrac{2 \times 5}{7 \times 8} $ $ \phantom{ \dfrac{2}{7} \times \dfrac{5}{8}} = \dfrac{10}{56} $ The numerator and denominator have a common divisor of $2$, so we can simplify: $ \dfrac{10}{56} = \dfrac{10 \div 2}{56 \div 2} = \dfrac{5}{28} $